System and method for accurate negative bias temperature instability characterization

ABSTRACT

Methods and systems are provided for characterizing the negative temperature bias instability of a transistor. A bias voltage is maintained at a drain terminal of the transistor during a test period. A stress voltage is maintained at a gate terminal of the transistor during the test period, such that the stress voltage is applied concurrently with the bias voltage. At least one characteristic of the transistor is measured at periodic intervals during the stress period to determine a degradation of the at least one characteristic caused by the stress voltage until a termination event occurs.

TECHNICAL FIELD

The present invention relates generally to electrical circuits, and moreparticularly to systems and methods for characterizing negative biastemperature instability of a transistor.

BACKGROUND OF THE INVENTION

Negative bias temperature instability is the tendency of a p-type metaloxide semiconductor (PMOS) transistor to degrade in performance when itsgate terminal is biased negatively relative to the remaining terminalsof the transistor over time. Negative bias temperature instability canincrease the required threshold voltage of the transistor gate anddecrease the drive current of the transistor. As a result, thisinstability has become one of the dominant reliability concerns inadvanced complementary metal oxide semiconductor (CMOS) processes.Characterizing the effects of negative bias temperature instability on agiven model of transistor is thus important in predicting an operationallifetime for the transistor and the products in which it is utilized.

One methodology for characterizing a negative bias temperatureinstability associated with a transistor includes connecting the source,drain, and body terminals of the transistor to ground. A stress voltageexceeding the normal operating voltage (in magnitude) of the transistoris then applied to the gate terminal of the transistor for a desiredperiod. The stress voltage is removed from the gate terminal after adesired period. To measure the effects of the applied stress, a biasvoltage (typically the operating voltage) is applied to the drainterminal and the current produced across the transistor by the biasvoltage is measured. The bias voltage is then removed and the stress isreapplied. This cycle repeats until a desired number of cycles arecompleted.

A problem associated with the described methodology is that duringmeasurements, the stress voltage to the gate is discontinued for a shorttime for each drain current measurement. During this time, an annealingeffect associated with the transistor produces a significant recovery inthe characteristics of the transistor, effectively reversing thedegradation by a small amount. This recovery provides a source of errorin characterizing the instability produced in the transistor. Further,the length of the delay is not standard between various testing methods,making it difficult to compare results obtained by different methods.

SUMMARY OF THE INVENTION

In accordance with one aspect of the present invention, a method forcharacterizing the negative temperature bias instability of a transistoris provided. A bias voltage is maintained at a drain terminal of thetransistor during a test period. A stress voltage is maintained at agate terminal of the transistor during the test period, such that thestress voltage is applied concurrently with the bias voltage. At leastone characteristic of the transistor is measured at periodic intervalsduring the stress period while maintaining the stress voltage at thegate terminal to determine a degradation of the at least onecharacteristic caused by the stress voltage until a termination eventoccurs.

In accordance with another aspect of the present invention, a system isprovided for characterizing the negative temperature bias instability ofa transistor. A first switch connects a gate terminal of the transistorto a first voltage source. A second switch connects a drain terminal ofthe transistor to a second voltage source. A measuring device measuresat least one characteristic of transistor. A system control controls thefirst switch, the second switch, and the measuring device, the systemcontrol maintaining the second switch in a closed position for a testingperiod. The system control directs the measuring device to make periodicmeasurements of the current at the drain terminal during the testingperiod.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other aspects of the present invention will becomeapparent to those skilled in the art to which the present inventionrelates upon reading the following description with reference to theaccompanying drawings.

FIG. 1 illustrates an apparatus for characterizing a negativetemperature bias associated with a transistor in accordance with anaspect of the present invention.

FIG. 2 is a line graph illustrating the annealing effect associated withnegative temperature bias instability.

FIG. 3 illustrates a methodology for characterizing a bias temperatureinstability associated with a transistor.

FIG. 4 illustrates an exemplary methodology for characterizing a biastemperature instability associated with a transistor.

FIG. 5 illustrates a line graph of a number of threshold voltagedegradation values plotted on a logarithmic scale.

FIG. 6 illustrates an exemplary system characterizing a negativetemperature bias associated with a transistor in accordance with anaspect of the present invention.

DETAILED DESCRIPTION

The present invention relates to systems and methods for characterizingthe negative bias temperature instability of a transistor. In accordancewith an aspect of the present invention, a bias voltage can bemaintained at the drain terminal of the transistor during a test period.A relatively large, negative stress voltage is applied to the gateterminal of the transistor. The current across the transistor can bemeasured at the drain terminal at selected intervals during the testperiod with no interruption of the stress voltage on the gate terminalto characterize the instability introduced by the stress voltage. Theeffects of a normal operating voltage on the transistor can beextrapolated from the measurements taken under stress.

FIG. 1 illustrates an apparatus 50 for characterizing a negativetemperature bias associated with a transistor 52 in accordance with anaspect of the present invention. The transistor 52 is connected into theapparatus such that its body terminal 54 and source terminal 56 areconnected to ground. The drain terminal 58 of the transistor 52 isconnected to a first voltage source providing a comparatively small biasvoltage through a first switch 62. The gate terminal 64 of thetransistor 52 is connected to a second voltage source providing a stressvoltage through a second switch 66. A measuring device 68 can beconnected in an appropriate manner between the drain terminal 58 and thefirst switch 62.

Prior to characterizing a transistor, initial measurements for variouscharacteristics of the transistor can be taken. For example, initialvalues for the threshold voltage for the transistor gate, the current atthe drain terminal generated by a bias voltage across the transistorduring both linear and saturated operation, and the transconductance ofthe transistor. These initial values can be determined by any suitablemeans. The determined initial values are then recorded for analysis at asystem control 70. It will be appreciated that the system control 70 canbe implemented as dedicated hardware and/or as computer softwareexecuted by a general purpose processor.

Once the initial measurements have been made, the system control 70 candirect the first and second switches 62 and 66 to assume a closedposition as to provide the stress voltage to the gate terminal 64 andthe bias voltage to the drain terminal 58. The switches 62 and 66 remainclosed for the duration of the testing, such that bias and stressvoltages are applied to their respective terminals uniformly throughoutthe testing. The stress voltage can be selected to exceed a normaloperating voltage associated with the gate terminal of the transistor 52as to accelerate the degradation of the transistor. For example, thetransistor 52 may have an operating voltage of one and one-half volts.The selected stress voltage can be around two or two and one-half voltsas to increase the rate of degradation of the transistor 52. The rate ofdegradation under a normal operation can be determined from the rate ofdegradation under the stress voltage. The bias voltage is generally arelatively small voltage used to produce a small level of current at thedrain terminal. For a sufficiently small bias voltage, it has beendetermined empirically that does not affect the rate of degradation ofthe transistor, allowing the voltage to be applied throughout thetesting process.

Measurements of the transistor characteristic can be taken at desiredintervals at the measurement device 68 to determine the degradation ofthe transistor characteristic over time. Since the bias voltage isconstant for the duration of the characterization process, the decreasein measured drain current over time is indicative of instabilityproduced in the transistor by the negative stress voltage. Thedegradation shown in transistor characteristics roughly follows a powerlaw curve, and in an exemplary embodiment, the measurements can be takenat exponentially increasing intervals (e.g., a measurement can be takenat every power of ten) to more efficiently illustrate the degradation ofthe transistor. An advantage of the illustrated apparatus is itsavoidance of the annealing effect associated with the testing process.Since the stress voltage is maintained throughout the testing process,the annealing effect is eliminated.

The transistor characteristic measurements can be provided to the systemcontrol 70 for analysis. The system control 70 can determine thedegradation of the characteristic over time under the stress voltage anddetermine from this how the transistor would degrade at a normaloperating gate voltage. For example, expected rates of degradationduring normal operation can be determined for a threshold voltageassociated with the gate terminal, a transconductance of the transistor,a mobility of the transistor, and the drain current produced during bothlinear and saturated operation. This can be accomplished, for example,by translating the degradation in the characteristic into an expecteddegradation in the gate threshold voltage for each stress voltage, andan expected gate threshold voltage degradation values for a standardvoltage can be extrapolated from these measurements according to a powerlaw relationship between the stress voltage and the threshold voltagedegradation. Other characteristics at a normal operating voltage can bedetermined according to their relationship to the determined thresholdvoltage.

FIG. 2 is a line graph 80 illustrating the annealing effect associatedwith negative temperature bias instability. The horizontal axis 82 ofthe graph represents time within a testing period. The vertical axis 84represents a degree of degradation in each transistor, in arbitraryunits. A first transistor, represented by a first line 86, is subjectedto a negative stress voltage of 3.1 volts at its gate terminal for theduration of the testing period. A second transistor, represented by asecond line 88, is stressed with a negative stress voltage of 3.1 voltsduring a first stress portion 90 of the testing period. The stress isremoved during a delay portion of the testing period 92, and reappliedduring a second stress portion of the testing period 94, in which thenegative stress voltage is reapplied.

The first transistor 86 illustrates a smooth degradation with a powerlaw relationship over time, as would be expected for a transistor underconstant stress. The second transistor 88 exhibits a similar degradationduring the first stress period 90. Once the stress is removed in thedelay period 92, however, the second transistor 86 experiences anannealing, or recovery effect, and the degradation is reduced. Thedegradation returns when the stress is reapplied to the secondtransistor 88 during the second stress period 94, but the level ofdegradation of the second transistor 88 remains lower than the level ofdegradation in the first transistor 86. Accordingly, the degradationexperienced by the second transistor 88 will not be fully representativeof a transistor under constant stress. Therefore, a lifetimedetermination based on the degradation of the second transistor 88 wouldbe inaccurate.

Referring now to FIGS. 3 and 4, there is illustrated a methodology 100in accordance with an aspect of the present invention. While, forpurposes of simplicity of explanation, a methodology is shown anddescribed as executing serially, it is to be understood and appreciatedthat the present invention is not limited by the order shown, as someaspects may, in accordance with the present invention, occur indifferent orders and/or concurrently from that shown and describedherein. Moreover, not all features shown or described may be needed toimplement a methodology in accordance with the present invention.Additionally, such methodology can be implemented in hardware (e.g., oneor more integrated circuits), software (e.g., running on a DSP or ASIC)or a combination of hardware and software.

FIG. 3 illustrates a methodology 100 for characterizing a biastemperature instability associated with a transistor. The methodology100 begins at 102 where initial measurements of the transistor aretaken. The initial measurements characterize the device prior to theapplication of a stress at the gate terminal. For example, the draincurrent and threshold voltage of the device can be measured duringlinear and saturated modes of operation of the transistor. Similarly,other parameters, such as the transconductance and mobility of thetransistor can be measured or determined from other measured data. At104, the source and body terminals of the transistor are connected toground. At 106, a small bias voltage is applied to the drain terminal ofthe transistor. In accordance with an aspect of the present invention,the bias voltage will be maintained at the drain terminal through thetesting period. The bias current can be kept small, such that thetransistor is operating in a linear mode. A stress voltage is thenapplied to the gate terminal of the transistor at 108. It will beappreciated that the stress voltage can significantly exceed theexpected operating voltage of the transistor.

At 110, a first measurement period is selected for the test. The firstmeasurement period controls the time until a first measurement is madein the system. In one example, the first measurement can be made onesecond after the stress voltage is applied to the gate terminal. At 112,a measurement of a transistor characteristic, such as the current at thedrain terminal of the transistor, is made at the end of the selectedtime period with no interruption of the stress voltage on the gateterminal. It is then determined if a termination event has occurred at114. Available termination events will vary with the application, butthey can include the passage of a predetermined period of time, athreshold value for the measured characteristic, or the complete failureof the transistor.

If it is determined that no termination event has occurred (N), themethodology continues to 116, where a new measurement period isselected. The selection of measurement periods will vary with thedesired application. In an exemplary embodiment, the various measurementperiods are selected as to produce a base ten exponential progression ofmeasurement periods. For example, a first period can comprise onesecond, a second period can comprise nine seconds, a third period cancomprise ninety seconds, and so on, such that each measurement is takenat a time corresponding to a power of ten. Once the period is selected,the methodology returns to 112 to take a measurement at the end of theselected period.

If it is determined that a termination event has occurred (Y), themethodology advances to 118, where the expected characteristics of thetransistor under normal operation are determined from the measureddegradation in the measured characteristic under constant stress. Forexample, a measured degradation in the drain current in linear modeunder the stress voltage can be used to derive the expected rate ofdegradation of the linear drain current under normal operation. In anexemplary implementation, a transistor can be tested at several stresslevels. The amount of time necessary to degrade the transistor to agiven level of drain current at each stress level can be plotted aslifetime values, and the lifetime of the transistor at an operatingvoltage can be extrapolated from the plot. This is facilitated by thefact that the lifetime of a transistor decreases according to aexponential function of the stress voltage utilized.

In another exemplary embodiment, the expected rate of degradation in thethreshold voltage for the transistor and the expected rate ofdegradation in drain current associated with operation in saturation canbe determined in from a measured degradation in drain current duringlinear operation of the transistor. It will be appreciated that, inaccordance with the present invention, the linear drain current can bemeasured during testing without interrupting the stress voltage at thedrain terminal. Accordingly, instead of interrupting the stress voltageto measure the threshold voltage and drain current at saturation, thecharacteristics can be derived from the measured degradation in thelinear mode drain current without interruption of the gate voltage. Therelationship between the degradation in the linear drain current and thedegradation in the threshold voltage can be expressed as follows:

$\begin{matrix}{\frac{\delta\; I_{DLIN}}{I_{DLIN}} \approx \frac{{- \delta}\; V_{T}}{V_{G} - V_{T}}} & {{Eq}.\mspace{20mu} 1}\end{matrix}$

where δI_(DLIN) is the change in the linear drain current during stress,I_(DLIN) is the initial linear drain current, δV_(T) is the expectedchange in the threshold voltage, V_(T) is the initial threshold voltage,and V_(G) is stress voltage applied to the transistor gate.

The relationship between the degradation of the linear drain current andthe expected degradation of the drain current at saturation can beexpressed as follows:

$\begin{matrix}{\frac{\delta\; I_{DSAT}}{I_{DSAT}} \approx {\theta\frac{{- \delta}\; V_{T}}{V_{G} - V_{T}}} \approx {\theta\frac{\delta\; I_{DLIN}}{I_{DLIN}}}} & {{Eq}.\mspace{20mu} 2}\end{matrix}$

where δI_(DSAT) is the expected change in the drain current atsaturation during stress, I_(DSAT) is the initial drain current atsaturation, δI_(DLIN) is the change in the linear drain current duringstress, I_(DLIN) is the initial linear drain current, δV_(T) is theexpected change in the threshold voltage, V_(T) is the initial thresholdvoltage, V_(G) is stress voltage applied to the transistor gate, and θis a function of the transistor channel length that typically rangesbetween one and two.

FIG. 4 illustrates an exemplary methodology 130 for characterizing abias temperature instability associated with a transistor. Themethodology begins at 132, where the degradation in the drain currentduring linear operation is measured as a function of time for a stressvoltage. This can be accomplished by maintaining a bias voltage at thedrain terminal of the transistor and a stress voltage is maintained atthe gate terminal of the transistor during a test period. The current atthe drain terminal is measured at periodic intervals during the stressperiod to determine a degradation of the drain current at various pointsin time. For example, measurements can be taken at a time associatedwith each power of ten (e.g., one second, ten second, one-hundredsecond, etc.) to better illustrate of the power law degradation of thetransistor over time.

Once these values have been determined, the methodology advances to 134,where the drain current degradation measurements are translated tothreshold voltage degradation measurements. A corresponding thresholdvoltage degradation can be calculated from a drain current degradationmeasured for a given stress voltage and time interval according to thefollowing relationship:

$\begin{matrix}{\frac{\delta\; I_{DLIN}}{I_{DLIN}} \approx \frac{{- \delta}\; V_{T}}{V_{G} - V_{T}}} & {{Eq}.\mspace{20mu} 3}\end{matrix}$

where δI_(DLIN) is the change in the linear drain over a given timeinterval for a given stress voltage, I_(DLIN) is the initial lineardrain current, δV_(T) is the expected change in the threshold voltageover a given time interval for a given stress voltage, V_(T) is theinitial threshold voltage, and V_(G) is stress voltage applied to thetransistor gate.

At 136, the expected threshold degradation at other stress voltages isextrapolated from the calculated values at the original stress voltage.The expected degradation for a given transistor can be expressed as afunction of stress voltage and time as follows

$\begin{matrix}{{\Delta\; V_{T}} = {C\;{\mathbb{e}}^{{- E_{A}}/{kT}}{\mathbb{e}}^{\beta\; V_{G}}{t^{n}:}}} & {{Eq}.\mspace{20mu} 4}\end{matrix}$where C is a transistor dependent constant, β is a voltage accelerationconstant associated with the transistor, E_(A) is an activation energyassociated with the transistor, k is the Boltzmann constant, T is theabsolute temperature, V_(G) is the voltage applied at the gate terminal,t is the time the voltage is applied, n is a time exponent associatedwith the transistor, and ΔV_(T) is the change in the threshold voltage.

The power law relationship between the threshold voltage degradation andthe stress time for a given stress voltage is illustrated in FIG. 5.FIG. 5 illustrates a line graph 140 of a number of threshold voltagedegradation values plotted on a logarithmic scale. The horizontal axis142 represents the time for which the transistor has been stressed. Thevertical axis 144 represents the degradation (e.g., increase) in thethreshold voltage of the transistor. It will be appreciated thatmeasurements of the degradation of the transistor over time form a line146 having a slope equal to a time exponent associated with thetransistor.

Returning to the illustrated methodology of FIG. 4, it is possible toextrapolate the degradation in the threshold voltage at a normal gatevoltage from the calculated degradation at stress voltage using thepower law relationship. Once this value is obtained, the methodologyadvances to 138, where the extrapolated value for the threshold voltageis used to determine one or more additional parameters for thetransistor. For example, the useful lifetime of the transistor can beobtained by selecting an acceptable level of threshold voltagedegradation and determining the time it will take the transistor todegrade to that level for a given operating voltage. Similarly, arelationship between the threshold voltage degradation and a degradationin the drain current over a period of time during saturated operation ofthe transistor can be expressed as follows:

$\begin{matrix}{\frac{\delta\; I_{DSAT}}{I_{DSAT}} \approx {\theta\frac{{- \delta}\; V_{T}}{V_{G} - V_{T}}}} & {{Eq}.\mspace{20mu} 5}\end{matrix}$where δI_(DSAT) is the expected change in the drain current over aninterval at saturation for a gate voltage V_(G), I_(DSAT) is the initialdrain current at saturation, δV_(T) is the expected change in thethreshold voltage over the same interval, V_(T) is the initial thresholdvoltage, and θ is a function of the transistor channel length thattypically ranges between one and two.

Other such relationships will be appreciated by those skilled in theart. Once the appropriate characteristics have been determined, themethodology 130 terminates.

FIG. 6 illustrates an exemplary system 150 for characterizing negativebias temperature instability in a transistor in accordance with thepresent invention. The system includes a testing apparatus 152 thatincludes the physical apparatus for applying stress voltages and takingdrain current measurements from the transistor. Accordingly, the testingapparatus can comprise one or more voltage sources, switches, andmeasurement devices (e.g., ammeters).

In the illustrated implementation, the system control 154 comprises acomputer 156 which has a processor 160 and memory 162. The computer 156can be operatively connected to one or more input and output devices toallow a human operator to interact with the system, such as a printer164, a keyboard 165, a mouse 166 and a display 167. The computer 156 canbe implemented as any suitable general purpose computer.

The processor 160 is operatively coupled to the testing apparatus 152via an instrument interface 170. The instrument interface 170 includeone or more components for interpreting data from the testing apparatus152 and generating electrical commands to the various components of thetesting apparatus (e.g., ammeter, switches). The processor 160 providesappropriate commands to the instrument interface 170 according to aprocess control program 172 stored in the memory. As measurement data isreceived at the computer 156 it is analyzed at the processor 160according to a measurement translation program 174 stored in memory. Themeasurement translation program 174 provides the functionality forconverting the measured characteristics from the testing apparatus 152into lifetime predictions for one or more characteristics of thetransistor. For example, the testing can be performed for one or morestress voltages, and a degradation in the drain current can be measuredfor each. The degradation in the drain current can be translated into anexpected degradation in the gate threshold voltage for each stressvoltage, and an expected gate threshold voltage degradation values for astandard voltage can be extrapolated from these measurements accordingto a power law relationship between the stress voltage and the thresholdvoltage degradation. Other characteristics at a normal operating voltagecan be determined according to their relationship to the determinedthreshold voltage.

What has been described above includes exemplary implementations of thepresent invention. It is, of course, not possible to describe everyconceivable combination of components or methodologies for purposes ofdescribing the present invention, but one of ordinary skill in the artwill recognize that many further combinations and permutations of thepresent invention are possible. Accordingly, the present invention isintended to embrace all such alterations, modifications, and variationsthat fall within the spirit and scope of the appended claims.

1. A system for characterizing the negative temperature bias instabilityof a transistor, comprising: a first switch that connects a gateterminal of the transistor to a first voltage source; a second switchthat connects a drain terminal of the transistor to a second voltagesource; a measuring device that measures at least one characteristic oftransistor; and a system control that controls the first switch, thesecond switch, and the measuring device, the system control maintainingthe second switch in a closed position for a testing period anddirecting the measuring device to make periodic measurements of the atleast one transistor characteristic during the testing period.
 2. Thesystem of claim 1, the first voltage source providing a first voltagethat is greater than a normal operating voltage associated with the gateterminal of the transistor.
 3. The system of claim 1, the system controlmaintaining the first switch in a closed position for the testing periodas to substantially eliminate annealing effects within the transistorduring the desired testing period.
 4. The system of claim 1, theperiodic measurements being separated by exponentially increasingintervals.
 5. The system of claim 1, the system control determining therate of degradation associated with a normal operating voltage at thegate terminal for the at least one characteristic of the transistor fromthe periodic measurements of the at least one characteristic.
 6. Asystem for characterizing the negative temperature bias instability of atransistor, comprising: means for maintaining a uniform bias voltage ata drain terminal of the transistor for a testing period during saidcharacterization of the negative temperature bias instability; means formaintaining a uniform stress voltage at a gate terminal of thetransistor for the testing period; and means for measuring a degradationin a characteristic of the transistor during the testing period; whereinthe transistor is operating in a linear mode under stress conditions. 7.The system of claim 6, further comprising means for controlling at leastone of the means for maintaining a stress voltage, the means formaintaining a bias voltage, and the means for measuring.
 8. The systemof claim 7, the means for controlling comprising means for extrapolatingat least one desired characteristic of the transistor associated with anormal operating voltage from the measured degradation in characteristicof the transistor.